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So, rubber's viscoelastic characters are researched by the characteristic nomography method in this article, when the stress wave transmits in rubber. And we get the stress'arithmetic solution and strain's arithmetic solution of any place of rubber parts at any time under the action of impact load.

本文又通过特征线解法，分析了橡胶在应力波传播过程中的粘弹性特性，得出了在冲击载荷作用下，橡胶部件的任意部位在任意时刻下的应力、应变数值解法。

On the basis of Venigalla\'s work,we adopted two path-based algorithms, namely,gradient projection algorithm and disaggregated simplicial decomposition algorithm to solve nonadditive path cost traffic assignment problem under different engine operating modes.We compared the above two algorithms in a network example which showed that compared with the traditional Frank-Wolfe algorithm, the two path-based algorithms had a more quicker convergency while getting optimal solution,and it can obtain a satisfying solution in most cases.

2在Venigalla等人研究工作的基础上，分别采用基于路径的梯度投影算法(gradient projection，GP)和基于路径的非集计的单纯分解算法(disaggregated simplicial decomposition，DSD)来求解考虑不同发动机启动模式下，具有非可加路径费用的交通分配问题，在实例计算中比较了这两种算法的计算性能。

This course consist of the following contents: the basic law of chemistry reaction, Chemical Thermodynamics, Chemical Equilibrium, chemical dynamics, modern basic knowledge about substance structure theory, the four ionic equilibrium in the water solution, Colligative Properties of Dilute Nonelectrolyte Solution, and Colloid.

本课程主要包含以下内容：化学反应的基本规律、介绍化学热力学、化学平衡、化学动力学基本原理、基本知识。近代物质结构理论基础知识。水溶液中的四大离子平衡。稀溶液通性和胶体溶液基本知识。

Later, we estimate our variational functional to get a nontrivial solution of the new equation and so the second solution for is obtained.

然后我们利用函数平移将原来的非齐次边界问题转化为奇次边界问题，验证了其对应的变分泛函满足不带条件的山路引理的两个条件，并给出了泛函临界点存在的一个充分条件，最后对具体的变分泛函进行估计，得到了新方程非平凡解的存在性结果，从而得到了原方程第二个正解的存在性结果。

The main results and novelties of the paper are as follows:Firstly, we study the existence of nontrivial solution for the following nonlinear equations with singular pontential By using variational methods and critical point theory, we construct linking type critical value of this kind of singular elliptic equations, with the properties of the eigenvalue, we estimate the critical value and prove the local condition holds to show the existence of the nontrivial solution.

论文的创新点及主要结果如下：首先研究有界区域上具有奇异位势的非线性方程的非平凡解的存在性，运用变分方法与临界点理论，构造这一类奇异椭圆方程的环绕型临界值，并由特征值的性质给出临界值的估计，同时证明局部条件成立，最终证明方程非平凡解的存在性。

The birth rate of the population is assumed to be a bifurcation parameter and nontrivial nonnegative steady-state solution bifurcated from the trivial steady-state solution has been obtained with the bifurcation theory.

应用分歧理论讨论一类单种群模型的非负定态解，并对该解的稳定性进行了分析。

Since two curves have the same coordinates and unit normal vector at the contacting point, the problem of the mesh of two planar curves is transformed into an ordinary differential equation by vector analysis. We have the solution to the equation by numerical method and computer calculation. After repeating the way of computing the solution to the equation, we have the contacting points.

因两曲线於接触点的位置相同，单位法线向量相等，由向量分析使曲线接触问题转变为常微分方程式，藉助数值计算与电脑运算得到方程式解，重覆计算方程式的解即可得每一接触点的位置。

The existence of global weak solution for a class of generalized Ginzburg-Landau equations with an inhomogeneous boundary condition was studied. Some integral indentities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained.

研究具非线性边界条件的一类广义Ginzburg＿Landau方程解的整体存在性·推导了Ginzburg＿Landau方程的非齐次初边值问题光滑解的几个积分恒等式，由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计；通过逼近技巧、先验估计和取极限方法证明了Ginzburg＿Landau方程的非齐次初边值问题整体弱解的存在性

Based on these results it is clear that the crosslinking system with low polymer concentration is different from normal polymer solution or gel dispersion, therefore, the crosslinking system is defined as a linked polymer solution.

因此，将此低浓度交联体系定义为交联聚合物溶液，以区别于一般聚合物溶液和凝胶分散体。

For the LS problem, the method of normal equations needs less computation but its computed solution has poor accuracy. If QR factorization is used, more accurate solution can be got. However, its computation is nearly as twice as the method of normal equations.

对于线性最小二乘问题，混合方法的提出是企图在法方程法与QR分解方法之间取得某种平衡，希望能够节省计算量又同时保持计算解达到较高精度，但后者在理论上并未得到证明。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷